Geodesic
Stability of flat thermal flux in a slab reactor
Applications of Mathematics, Tome 13 (1968) no. 5, pp. 367-375
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Using the qualitative theory of differential equations the equivalence of the boundary value and the Cauchy's initial value problem is demonstrated for the slab flat flux reactor. It is found that there exists an interval of the initial (central) fuel concentrations for which the initial value problem (with two algebraic conditions) describes a critical flat flux reactor while solutions outside this interval describe undercritical systems of a nonmultiplying medium.
Using the qualitative theory of differential equations the equivalence of the boundary value and the Cauchy's initial value problem is demonstrated for the slab flat flux reactor. It is found that there exists an interval of the initial (central) fuel concentrations for which the initial value problem (with two algebraic conditions) describes a critical flat flux reactor while solutions outside this interval describe undercritical systems of a nonmultiplying medium.
DOI : 10.21136/AM.1968.103183
Classification : 82-34
Keywords: numerical analysis 
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Bartošek, Václav; Zezula, Rostislav. Stability of flat thermal flux in a slab reactor. Applications of Mathematics, Tome 13 (1968) no. 5, pp. 367-375. doi: 10.21136/AM.1968.103183

[1] V. Bartošek, R. Zezula: Flat Flux in a Slab Reactor with Natural Uranium. Journal of Nucl. Energy Pt A/B 20, 129-134, (1966). | DOI

[2] E. F. Beckenbach: Modern Mathematics for the Engineer. McGraw-Hill Book Соmр. New York - Toronto - London. | Zbl

[3] S. Lefshetz: Differential Equations: Geometric Theory. Interscience Publishers, London 1957. | MR

[4] R. Bellman: Stability Theory of Differential Equations. London 1953. | MR | Zbl

[5] J. Roček: Private communication, 1966.

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